Adaptive ISO-Gain pre-distortion for an RF power amplifier operating in envelope tracking

ABSTRACT

The output of a Radio Frequency (RF) Power Amplifier (PA) is sampled and down-converted, and the amplitude envelope of the baseband feedback signal is extracted. This is compared to the envelope of a transmission signal, and the envelope tracking modulation of the RF PA supply voltage V CC  is adaptively pre-distorted to achieve a constant ISO-Gain (and phase) in the RF PA. In particular, a nonlinear function is interpolated from a finite number gain values calculated from the feedback and transmission signals. This nonlinear function is then used to pre-distort the transmission signal envelope, resulting in a constant gain at the RF PA over a wide range of supply voltage V CC  values. Since the gains are calculated from a feedback signal, the pre-distortion may be recalculated at event triggers, such as an RF frequency change. Furthermore, the method improves nonlinearity in the entire transmitter chain, not just the RF PA.

FIELD OF INVENTION

The present invention relates generally to RF transmitters, and inparticular to an adaptive ISO-Gain pre-distortion for an RF poweramplifier operating in envelope tracking mode.

BACKGROUND

Mobile electronic communication devices—including cellular telephones,pagers, smartphones, remote monitoring and reporting devices, and thelike—have dramatically proliferated with the advance of the state of theart in wireless communication networks. Many such devices are powered byone or more batteries, which provide a Direct Current (DC) voltage. Onechallenge to powering electronic communication devices from batteries isthat the battery does not output a stable DC voltage over its usefullife (or discharge cycle), but rather the DC voltage decreases until thebattery is replaced or recharged. Also, many electronic communicationdevices include circuits that operate at different voltages. Forexample, the Radio Frequency (RF) circuits of a device may require powersupplied at a different DC voltage than digital processing circuits.

A DC-DC converter is an electrical circuit typically employed to convertan unpredictable battery voltage to one or more continuous, regulated,predetermined DC voltage levels, and thus to provide stable operatingpower to electronic circuits. Numerous types of DC-DC converters areknown in the art. The term “buck” converter is used to describe a DC-DCconverter that outputs a lower voltage than the DC source (such as abattery); a “boost” converter, also called a step-up, is one thatoutputs a higher voltage than its DC input. Both boost and buckconverters may be implemented as switched mode power supplies (SMPS), inwhich energy is transferred from a source, such as battery, to a storagecomponent, such as an inductor or capacitor, at a high frequency throughtransistor switches.

Supplying power to an RF power amplifier (PA) of an electroniccommunication device is particularly challenging. The efficiency of anRF PA varies with the amplitude of the transmission signal to beamplified. Maximum efficiency is achieved at full power, and dropsrapidly as the transmission signal amplitude decreases, due totransistor losses accounting for a higher percentage of the total powerconsumed. The loss of efficiency may be compensated by a technique knownas “envelope tracking,” in which the output of a DC-DC converter, andhence the voltage supplied to the PA, is not constant, but is modulatedto follow the amplitude modulation of the transmission signal. In thismanner, at any given moment, the power supplied to the RF PA depends onthe amplitude of the signal being amplified. Such modulation of the RFPA power supply can dramatically improve power consumption efficiency.

FIG. 1 depicts the relevant RF output portion of an electroniccommunication device 10. A battery 12 provides a battery voltage V_(BAT)to an efficient, wide-bandwidth envelope-tracking power supply 14 thatmodulates the supply voltage of the RF PA 16. The RF PA 16 outputs anamplified RF signal for transmission from the device 10 on one or moreantenna 18. The modulated voltage V_(CC)(t) output by the dynamic powersupply 14 should be capable of tracking a rapidly varying referencevoltage. As such, the power supply 14 must meet certain bandwidthspecifications. The required bandwidth depends on the specifications ofthe network(s) in which the RF PA 16 is used. For example, the requiredbandwidth exceeds 1 MHz for EDGE systems (8PSK modulation), and exceeds30 MHz for LTE20 (Long Term Evolution).

The design of transmitters 10 employing envelope tracking power supplies14 for RF PAs 16 is challenging, and requires the use of moresophisticated characterization techniques than is the case for designingtraditional, fixed supply power amplifiers. The fundamental outputcharacteristics of an RF PA 16 with an envelope tracking powersupply—power, efficiency, gain, and phase—depend on two control inputs:RF input signal power and the supply voltage V_(CC).

A typical envelope tracking system dynamically adjusts the supplyvoltage V_(CC) to track the RF input signal envelope at highinstantaneous power. In this case, the PA 16 operates with highefficiency in compression. The instantaneous supply voltage V_(CC)(t)primarily determines the PA 16 output characteristics. Unfortunately,this supply voltage modulation introduces an additional source ofdistortion that is due to the variations of PA 16 gain and/or phase as afunction of the supply voltage V_(CC). FIG. 2A depicts variations ingain (AM-AM), and FIG. 2B depicts variations in phase AM-PM) with supplyvoltage V_(CC) variations. In a conventional PA, supplied by a constantvoltage, these variations are only linked to the variation of the RFinput signal voltage.

FIG. 3A depicts the time-domain variations of the voltage V_(CC)supplied to a PA 16 by an envelope tracing power supply 14, and FIG. 3Bdepicts the corresponding time-domain variations in the gain of the PA16. These waveforms clearly show the dependency of the gain on supplyvoltage modulation. For example, large negative deviations, or drops, insupply voltage V_(CC) correspond to very large decreases in gain.Moreover, this dependency is a nonlinear one, being significantly morepronounced as the supply voltage V_(CC) is reduced. FIG. 4 depicts thePA 16 gain as a function of the supply voltage V_(CC), where again it isevident that low excursions of supply voltage V_(CC) correspond todramatic drops in the small signal gain of the RF PA 16. This modulationof the PA 16 gain impairs linearity of the PA 16.

In general, the transfer function for an amplified RF signal isV _(OUT)(V _(CC) ,V _(IN))=G _(PA)(V _(CC) ,V _(IN))·V _(IN)  (1)where V_(IN) is the magnitude of the RF PA 16 input signal,V_(OUT)(V_(IN),V_(CC)) is the magnitude of the output signal, V_(CC) isthe PA 16 instantaneous voltage from power supply 14, and finallyG_(PA)(V_(IN),V_(CC)) is the gain of the PA. The gain G_(PA), and hencethe output voltage V_(OUT), is a nonlinear function of V_(IN) andV_(CC). Ideally, the gain should be constant.

The nonlinear gain G_(PA) can be approximated by a two-dimensionalpolynomial.G _(PA)(V _(CC) ,V _(IN))=b ₀ +b ₁ V _(CC) +b ₂ V _(CC) ² + . . . +b_(β-1) V _(CC) ^(β-1) +b _(β) V _(CC) ^(β)

with:

$\begin{matrix}{{b_{0} = {c_{0_{1}} + {c_{1_{1}} \cdot V_{IN}} + \ldots + {c_{\alpha - 1_{1}} \cdot V_{IN}^{\alpha - 1}} + {c_{\alpha_{1}} \cdot V_{IN}^{\alpha}}}}{b_{1} = {c_{0_{2}} + {c_{1_{2}} \cdot V_{IN}} + \ldots + {c_{\alpha - 1_{2}} \cdot V_{IN}^{\alpha - 1}} + {c_{\alpha_{2}} \cdot V_{IN}^{\alpha}}}}\ldots{b_{\beta - 1} = {{c_{0_{\beta - 1}} \cdot V_{IN}} + \ldots + {c_{\alpha - 1_{\beta - 1}} \cdot V_{IIN}^{\alpha - 1}} + {c_{\alpha_{\beta - 1}} \cdot V_{IN}^{\alpha}}}}{b_{\beta} = {c_{0_{\beta}} + {c_{1_{\beta}} \cdot V_{IN}} + \ldots + {c_{\alpha - 1_{\beta}} \cdot V_{IN}^{\alpha - 1}} + {c_{\alpha_{\beta}} \cdot V_{IN}^{\alpha}}}}} & (2)\end{matrix}$

FIGS. 5A and 5B depict how laboratory measurements (circles) of PA 16gain vs. supply voltage V_(CC) and RF transmission signal voltage,respectively, can be interpolated using the 2-D polynomial (continuouslines). Note that the phase shift of the PA 16 could similarly bewritten this way and interpolated by a 2-D polynomial.

The term “ISO-Gain” is used herein as a generic, descriptive term todenote a constant gain (G_(ISO)) in an RF PA 16, which does not changein response to variations in V_(CC) and V_(IN). From equation (1), thegain can be written as:

$\begin{matrix}{{G_{PA}\left( {V_{CC},V_{I\; N}} \right)} = {\frac{V_{OUT}\left( {V_{CC},V_{IN}} \right)}{V_{IN}} = {\frac{V_{OUT}\left( {V_{CC},V_{IN}} \right)}{V_{CC}} \cdot \frac{V_{CC}}{V_{IN}}}}} & (3)\end{matrix}$

In envelope tracking operation the voltage V_(CC) (from the voltagesupply 14) is a linear replica of the envelope of an RF input signalmultiplied by a constant α. As a result:

$\begin{matrix}{{G_{PA}\left( {V_{CC},V_{IN}} \right)} = {\frac{V_{OUT}\left( {V_{CC},V_{IN}} \right)}{V_{CC}} \cdot \alpha}} & (4)\end{matrix}$

In order to obtain a constant gain G_(ISO) over variations in bothV_(CC) and V_(IN), the following condition must be met:

$\begin{matrix}{{{G_{PA}\left( {V_{CC},V_{IN}} \right)} = G_{ISO}}{{so},}} & (5) \\{G_{ISO} = {\frac{V_{OUT}\left( {V_{CC},V_{IN}} \right)}{V_{{CC}\;\_\;{pred}}} \cdot {\alpha.}}} & (6)\end{matrix}$

This condition can be fulfilled by modifying the shape of V_(CC) througha particular pre-distortion gain that depends on both V_(CC) and V_(IN):V _(CC) _(—) _(pred)(V _(CC) ,V _(IN))=V _(CC)·Gain_(pred)(V _(CC) ,V_(IN)).  (7)

Substituting equation (7) into equation (6) yields an expression of therequired pre-distortion gain:

$\begin{matrix}{{{Gain}_{pred}\left( {V_{CC},V_{IN}} \right)} = {\frac{\alpha}{G_{ISO}} \cdot \frac{V_{OUT}\left( {V_{CC},V_{IN}} \right)}{V_{CC}}}} & (8)\end{matrix}$FIG. 6 depicts the operation of ISO-Gain pre-distortion in the casewhere V_(CC) is constant and V_(IN) (or P_(IN)) varies. The nonlineargain applied to the supply voltage V_(CC) is depicted in the lowercurve, whereas the PA 16 gains with and without ISO-Gain pre-distortionare depicted in the upper two curves. The upper curve clearly shows thatISO-Gain operation allows maintaining the gain of the PA 16 relativelyconstant for a wide range of V_(IN) (or P_(IN)).

In practice, pre-distortion such as that depicted in FIG. 6 relies ontesting and calibrations performed at chip fabrication. Pre-distortionparameters are calculated, and stored in large look-up tables (LUT).During operation, pre-distortion perturbations are retrieved from theLUTs and applied to the power supply 14. Accuracy is proportional to thesize of the LUT; however, accuracy is limited because the necessarycomputation time is also proportional to the LUT size. Additionally,because all known envelope tracking RF PA power supply pre-distortion is“open-loop” and uses factory-generated values, the pre-distortionapplied cannot be recalculated over the life of the circuit, such as toaccount for shifts in RF frequency, output power, temperature, componentaging, and the like.

The Background section of this document is provided to place embodimentsof the present invention in technological and operational context, toassist those of skill in the art in understanding their scope andutility. Unless explicitly identified as such, no statement herein isadmitted to be prior art merely by its inclusion in the Backgroundsection.

SUMMARY

The following presents a simplified summary of the disclosure in orderto provide a basic understanding to those of skill in the art. Thissummary is not an extensive overview of the disclosure and is notintended to identify key/critical elements of embodiments of theinvention or to delineate the scope of the invention. The sole purposeof this summary is to present some concepts disclosed herein in asimplified form as a prelude to the more detailed description that ispresented later.

According to one or more embodiments described and claimed herein, anadaptive pre-distortion system and method does not rely on voluminousparameters, stored in large LUTs, generated from factory calibrations.Rather, the output of the RF PA is sampled and down-converted, and theamplitude envelope of the baseband feedback signal is extracted. This iscompared to the envelope of the transmission signal, and the envelopetracking modulation of the RF PA supply voltage V_(CC) is adaptivelypre-distorted to achieve a constant ISO-Gain in the RF PA. Inparticular, a nonlinear function is interpolated from a finite numbergain values calculated from the feedback and transmission signals. Thisnonlinear function is then used to pre-distort the transmission signalenvelope, resulting in a constant gain at the RF PA over a wide range ofsupply voltage V_(CC) values. Since the gains are calculated from afeedback signal, the pre-distortion may be recalculated at eventtriggers, such as an RF frequency change. Furthermore, the methodimproves nonlinearity in the entire transmitter chain, not just the RFPA.

One embodiment relates to an adaptive method of pre-distorting anenvelope tracking modulation of supply voltage for a RF PA. Theamplitude envelope of a complex baseband transmission signal iscalculating, and the complex baseband transmission signal is frequencyup-converted to RF. A supply voltage, output by a dynamic power supplyto a RF PA, is modulated in response to the amplitude envelope of thebaseband transmission signal. The RF transmission signal is amplified bythe RF PA receiving the modulated supply voltage. An RF feedback signalis sampled at the RF PA output, frequency down-converted to baseband,and an amplitude envelope of the baseband feedback signal is extracted.The amplitude envelope of the baseband feedback signal is compared withthe amplitude envelope of the baseband transmission signal, and themodulation of the supply voltage is pre-distorted in response to thecomparison so as to achieve a constant gain in the RF PA.

Another embodiment relates to an RF transmitter. The transmitterincludes a signal generator operative to generate a complex basebandtransmission signal; frequency up-converting mixers operative toup-convert the baseband transmission signal to RF; an RF PA operative toamplify the RF transmission signal; a dynamic power supply operative toprovide a supply voltage to the RF PA that is modulated to track anamplitude envelope of the baseband transmission signal; a feedback loopoperative to sample an RF feedback signal at the RF PA output andfrequency down-convert the RF feedback signal to baseband; and apre-distortion circuit operative to calculate the gain of the RF PAbased on the baseband feedback signal and the baseband transmissionsignal, and further operative to control the power supply to pre-distortthe modulated supply voltage so as to achieve a constant gain in the RFPA.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will now be described more fully hereinafter withreference to the accompanying drawings, in which embodiments of theinvention are shown. However, this invention should not be construed aslimited to the embodiments set forth herein. Rather, these embodimentsare provided so that this disclosure will be thorough and complete, andwill fully convey the scope of the invention to those skilled in theart. Like numbers refer to like elements throughout.

FIG. 1 is a functional block diagram of a conventional transmitteroutput, depicting envelope tracking.

FIG. 2A is a graph depicting variations in gain (AM-AM) with supplyvoltage V_(CC) variations in a conventional envelope tracking PA.

FIG. 2B is a graph depicting variations in phase AM-PM) with supplyvoltage V_(CC) variations in a conventional envelope tracking PA.

FIG. 3A is a graph depicting time-domain variations of the voltageV_(CC) supplied to a PA by a conventional envelope tracking powersupply.

FIG. 3B is a graph depicting the time-domain variations in the gain of aPA receiving a conventional envelope tracking supply voltage.

FIG. 4 is a graph depicting the PA gain as a function of the supplyvoltage V_(CC) for a conventional envelope tracking power supply

FIG. 5A is a graph depicting how laboratory measurements (circles) of PAgain vs. supply voltage V_(CC) can be interpolated using the 2-Dpolynomial (continuous lines).

FIG. 5B is a graph depicting how laboratory measurements of PA gain(circles) vs. RF PA input signal can be interpolated using the 2-Dpolynomial (continuous lines).

FIG. 6 depicts the operation of conventional ISO-Gain pre-distortion inthe case where V_(CC) is constant and V_(IN) varies.

FIG. 7 a functional block diagram of portions of an RF transmitteremploying an envelope tracking power supply with adaptive,feedback-based pre-distortion to achieve ISO-Gain for the PA, accordingto embodiments of the present invention.

FIG. 8 is a graph depicting a waveform of V_(CC)(t) as a function oftime, with a representative set of interpolation nodes.

FIG. 9 is a table depicting the calculation of coefficients to anonlinear function.

FIG. 10 is a flow diagram of an adaptive method of pre-distorting anenvelope tracking modulation of supply voltage for a RF PA.

FIG. 11A is a graph depicting the evolution of the RF PA supply voltageV_(CC)(t) over several iterations of the adaptive ISO-Gain method ofFIG. 10.

FIG. 11B is a graph depicting the evolution of the RF PA gain overseveral iterations of the adaptive ISO-Gain method of FIG. 10.

FIG. 12 is a graph depicting RF PA gain vs. supply voltage V_(CC)(t)over several iterations of the adaptive ISO-Gain method of FIG. 10.

FIG. 13 is a graph depicting RF PA phase vs. supply voltage V_(CC)(t)over several iterations of the adaptive ISO-Gain method of FIG. 10.

FIG. 14 is a graph depicting the output spectrum of the RF PA overseveral iterations of the adaptive ISO-Gain method of FIG. 10.

DETAILED DESCRIPTION

It should be understood at the outset that although illustrativeimplementations of one or more embodiments of the present disclosure areprovided below, the disclosed systems and/or methods may be implementedusing any number of techniques, whether currently known or in existence.The disclosure should in no way be limited to the illustrativeimplementations, drawings, and techniques illustrated below, includingthe exemplary designs and implementations illustrated and describedherein, but may be modified within the scope of the appended claimsalong with their full scope of equivalents.

FIG. 7 depicts a functional block diagram of relevant portions of an RFtransmitter 20 employing an envelope tracking power supply 14 withadaptive, feedback-based pre-distortion to achieve ISO-Gain for the PA16. The basic transmission blocks of the transmitter 20 are as depictedin FIG. 1: a battery 12 provides a slowly-varying DC voltage to a fastswitched mode power supply 14, which modulates the supply voltage V_(CC)provided to a power amplifier (PA) 16 based on the amplitude envelope ofan RF transmission signal (the PA 16 input). The PA 16 outputs anamplified RF output signal, through a duplexer 22, to an antenna 18 fortransmission. As known in the art, the duplexer 22 isolates thetransmitter 20 from a receiver circuit (not shown), and alternatelyconnects the antenna 18 to one of the transmitter 20 and receiver.

The transmitter 20 also includes conventional elements, including acomplex signal generator 22, such as a processor or Digital SignalProcessor (DSP) generating baseband, time-varying In-band (I) andQuadrature (Q) transmission signal components. These transmission signalcomponents are frequency up-converted to RF in mixers 24, by mixing withhigh frequency clock signals, phase-separated by 90° in a phase shifter26. The high frequency clock input to the phase shifter 26 is generatedby a source 28, such as a tunable voltage controlled oscillator (VCO),crystal oscillator, phase locked loop, or the like.

According to embodiments of the present invention, the transmitter 20includes a feedback path 29 and pre-distortion circuit 38 operative topre-distort an envelope tracking voltage V_(CC) output by the powersupply 14 to the RF PA 16, so as to achieve a constant ISO-Gain G_(ISO)at the RF PA 16. The feedback path 29 includes an attenuator 30 thattaps a fraction of the power of the RF output signal, generating an RFfeedback signal. The RF feedback signal is frequency down-converted bymixers 32, generating baseband I_(FB) and Q_(FB) components of afeedback signal. An extraction circuit 34 extracts the amplitudeenvelope of the baseband feedback signal, which is provided to thepre-distortion circuit 38.

The amplitude envelope of the baseband transmission signal is calculatedby an envelope circuit 36 from the real and imaginary parts of thecomplex transmission signal, and is also provided to the pre-distortioncircuit 38. The envelope circuit 36 may comprise part of the processor22. The pre-distortion circuit 38 processes the baseband feedback signalenvelope and that of the baseband transmission signal, and outputscontrol signals to the dynamic power supply 14 that modulate V_(CC) toachieve ISO-Gain in the PA 16. In one embodiment, the pre-distortioncircuit 38 multiplies the baseband transmission signal amplitudeenvelope by a nonlinear function, where the parameters of the nonlinearfunction are determined by calculation of the actual gain of the RF PA16 (e.g., the feedback signal envelope divided by the transmissionsignal envelope). The pre-distortion circuit 38 may comprise a statemachine, processor, DSP, or other computational circuit. Thepre-distortion circuit 38 may additionally be implemented as softwareexecuted on another processor, such as the signal generator 22.

In this manner, embodiments of the present invention achieve a constantISO-Gain in the RF PA 16, by using feedback of the RF PA output toadaptively pre-distort the envelope tracking supply voltage V_(CC)provided by power supply 14. Such adaptive ISO-Gain pre-distortion cancompensate distortions of the entire transmitter 20, allowing thelinearity constraints on DACs (not shown), mixers 24, and the RF PA 16to be lowered. Any distortion generated by the feedback loop 29 is notcompensated by the pre-distortion algorithm. The adaptive,feedback-based ISO-Gain pre-distortion may additionally compensatenon-linearity in the fast switched mode power supply 14. Furthermore,the dynamic control provided by adaptive pre-distortion does not dependon factory calibration results, and hence can account for operationalchanges, such as changes in RF frequency, output power, temperature,component aging, and the like. Additionally, large LUTs are not requiredto store voluminous calibration data, as in the case of open-looppre-distortion methods, and consequently high accuracy is achieved withlow latency and low computational complexity.

In one embodiment, the pre-distortion circuit 38 multiplies thereference amplitude envelope of the baseband transmission signal by anonlinear function to generate control signals for the power supply 14.In one embodiment, the nonlinear function is approximated by apolynomial. The coefficients of the polynomial are calculated (anddynamically updated) using information about the envelope of thebaseband feedback signal obtained from the feedback path 29. In thisembodiment, the transmitter 20 operates in closed-loop mode only duringthe calculation or update of the polynomial coefficients, which arestored in small LUTs. During operation, the transmitter 20 operates inopen-loop mode, using the calculated/updated polynomial coefficients. Attrigger events, such as the expiration of a periodic timer, oroperational events such as a transmission frequency change, thetransmitter 20 again goes into closed-loop mode to update the polynomialcoefficients based on the amplitude envelope of the baseband feedbacksignal.

In one embodiment, an algorithm for employing a polynomial-basednonlinear function in the pre-distortion circuit 38 includes threesteps. First, a measurement, or Learning, Sequence is performed. This isfollowed by an Interpolation Sequence. Finally, a Computation Sequenceis performed. The first two of these—Learning and Interpolation—areperformed only when an update of the polynomial coefficients is needed.

The Learning Sequence is performed when the transmitter 20 isoperational, i.e., transmitting a signal, such as a voice call. Thecomplex RF signal output by the PA 16 is sampled, down-converted tobaseband, and converted to I and Q format, in the feedback loop 29. Aconversion is then performed in extraction circuit 34 to obtain theamplitude envelope of the baseband feedback signal:ENV_(FB)(t)=√{square root over (I _(FB)(t)² +Q _(FB)(t)²)}{square rootover (I _(FB)(t)² +Q _(FB)(t)²)}  (9)

Among all measured samples, only N+1 values are selected and stored, fora polynomial of order N. These points are chosen as a function ofV_(CC), which is an image of the envelope of the baseband feedbacksignal:V _(CC)(t)=α√{square root over (I ²(t)+Q ²(t))}{square root over (I²(t)+Q ²(t))}  (10)

The samples selection is performed according to the following condition:If V _(CC)(t)=V _(CC,k)

store└ENV_(FB,k)┘ with 0≦k≦N  (11)where N is the order of the polynomial used to interpolate thepre-distortion function and V_(CC,k) are the interpolation points or“nodes.” FIG. 8 depicts a waveform of V_(CC)(t) as a function of time,with a representative set of interpolation nodes. The interpolationnodes may be equally spaced, and calculated using a simple equation.Alternatively, the interpolation nodes may be selected by other methods.One example of an interpolation node selection approach that minimizesinterpolation error is to select Chebyshev nodes. In this approach,

$\begin{matrix}{{V_{{CC},k} = {{\min\left( {V_{CC}(t)} \right)} + {{j \cdot \frac{{\max\left( {V_{CC}(t)} \right)} - {\min\left( {V_{CC}(t)} \right)}}{N}}\mspace{14mu}{with}}}}{0 \leq j \leq N}} & (12)\end{matrix}$where min(V_(CC)(t)) and max(V_(CC)(t)) are the minimum and maximumvalues of power supply modulation, respectively. These values must bedetected, or may be provided by the digital baseband signal generator22.

The Learning Sequence thus records the baseband feedback signal envelopeENV_(FB) and corresponding PA 16 supply voltage V_(CC) for each of aplurality of interpolation nodes. In one embodiment, the LearningSequence is preferably performed several times in order to filter thesamples through a mean value computation. In one embodiment, the meanvalues over V_(CC,k) and ENV_(FB,k) are calculated, preferably overmultiple measurement iterations.

In the Interpolation Sequence, the stored samples are used forinterpolating the pre-distortion function. That is, a nonlinear functionis generated that is a “best fit” curve to the sampled (V_(CC,k))ENV_(FB,k)) data points. In one embodiment, the nonlinear function ismodeled as a polynomial. In one embodiment, the interpolation isperformed using Newton's algorithm. Newton's algorithm is a knownmathematical function, which has the advantage that only multiply andsum mathematical operations are required for implementation.

The gain values to be interpolated are determined directly from thestored, sampled (V_(CC,k), ENV_(FB,k)) data points:

$\begin{matrix}{G_{{pred},k} = {{\frac{{ENV}_{{FB},k}}{V_{{CC},k}}\mspace{14mu}{with}\mspace{14mu} 0} \leq k \leq N}} & (13)\end{matrix}$

This pre-distortion gain must be normalized in order to neglect anyconstant gain (or attenuation) that could have been applied to thefeedback signal by the feedback loop 29:

$\begin{matrix}{G_{{pred},k} = {{{\frac{{ENV}_{{FB},k}}{V_{{CC},k}} \cdot \frac{\overset{\_}{V_{{CC},k}}}{\overset{\_}{{ENV}_{{FB},k}}}}\mspace{14mu}{with}\mspace{14mu} 0} \leq k \leq N}} & (14)\end{matrix}$where, in one embodiment, the average values were measured during theLearning Sequence.

After the gain values are calculated, a small table of (N+1)×2 is filledwith the interpolation inputs:

$\quad\begin{pmatrix}V_{{CC},0} & G_{{pred},0} \\\vdots & \vdots \\V_{{CC},{N - 1}} & G_{{pred},{N - 1}} \\V_{{CC},N} & G_{{pred},N}\end{pmatrix}$

Starting from these values, the gain pre-distortion function isinterpolated as a function of V_(CC). In one embodiment, the polynomialform of Newton's formula is utilized:

$\begin{matrix}{{G_{pred}\left( {V_{CC}(t)} \right)} = {\frac{\alpha}{G_{ISO}}\left\lbrack {g_{0} + {g_{1} \cdot \left( {{V_{CC}(t)} - V_{{CC},0}} \right)} + {g_{2} \cdot \left( {{V_{CC}(t)} - V_{{CC},0}} \right) \cdot \left( {{V_{CC}(t)} - V_{{CC},1}} \right)} + \ldots + {{g_{N} \cdot \left( {{V_{CC}(t)} - V_{{CC},0}} \right) \cdot \left( {{V_{CC}(t)} - V_{{CC},1}} \right)}\mspace{14mu}\ldots\mspace{14mu}\left( {{V_{CC}(t)} - V_{{CC},{N - 1}}} \right)}} \right\rbrack}} & (15)\end{matrix}$

One advantage of Newton's formula is that an N^(th)-degree polynomial,matching the N+1 data points {(x₀, y₀), (x₁, y₁), . . . , (x_(N),y_(N))}can be recursively obtained as the sum of the (N−1)^(th)-degreeNewton polynomial matching N data points {(x₀, y₀), (x₁, y₁), . . . ,(x_(N-1), y_(N-1))} and one additional term. See, for example, Won Y.Yang, et al., “Applied Numerical Methods Using Matlab,” WileyInterscience, 2005, the disclosure of which is incorporated herein byreference in its entirety. Thus,p _(N)(x)=a ₀ +a ₁·(x−x ₀)+a ₂·(x−x ₀)·(x−x ₁)+ . . .p _(N)(x)=p _(N-1) +a _(N)·(x−x ₀)·(x−x ₁) . . . (x−x _(N-1)) with p₀(x)=a ₀ =y ₀  (16)

The polynomial coefficients a₀, a₁, . . . , a_(n) can be calculated asfollows:

$\begin{matrix}{{a_{0} = y_{0}}{a_{1} = {\frac{y_{1} - a_{0}}{x_{1} - x_{0}} = {\frac{y_{1} - y_{0}}{x_{1} - x_{0}} \equiv {Df}_{0}}}}{a_{2} = {\frac{\frac{y_{2} - y_{1}}{x_{2} - x_{1}} - \frac{y_{1} - y_{0}}{x_{1} - x_{0}}}{x_{2} - x_{0}} = {\frac{{Df}_{1} - {Df}_{0}}{x_{2} - x_{0}} \equiv {D^{2}f_{0}}}}}} & (17)\end{matrix}$

On the other hand, the general formula for the calculation of the N^(th)coefficient a_(n) of a Newton polynomial function is:

$\begin{matrix}{a_{N} = {\frac{{D^{N - 1}f_{1}} - {D^{N - 1}f_{0}}}{x_{N} - x_{0}} \equiv {D^{N}f_{0}}}} & (18)\end{matrix}$

This is the “divided difference,” which can be obtained recursively fromthe second row of the table depicted in FIG. 9. The coefficientscalculation is quite simple and requires only few subtractions anddivisions to implement. Furthermore, this calculation is performed onlyonce during the Interpolation Sequence, to generate the nonlinearfunction from the sampled (V_(CC,k), ENV_(FB,k)) data points.

At the completion of the Interpolation Sequence, (N+1)values—representing the Newton's polynomial coefficients—replace themeasured samples in the table of values stored during the LearningSequence.

$\left. \begin{pmatrix}V_{{CC},0} & G_{{pred},0} \\\vdots & \vdots \\V_{{CC},{N - 1}} & G_{{pred},{N - 1}} \\V_{{CC},N} & G_{{pred},N}\end{pmatrix}\Rightarrow\begin{pmatrix}V_{{CC},0} & g_{0} \\\vdots & \vdots \\V_{{CC},{N - 1}} & g_{N - 1} \\V_{{CC},N} & g_{N}\end{pmatrix} \right.$

In the Computation Sequence, the polynomial coefficients g_(n) are usedto dynamically calculate the pre-distortion gain to be applied toV_(CC), using equation (15). That is, the pre-distortion circuit 38multiplies the baseband transmission signal amplitude envelope providedby reference circuit 36 “on the fly” by equation (15), using the storedvalues of (V_(CC,n), g_(n)). This calculation, which requires onlymultiplication and summing functions, is performed in open-loop mode,using the stored (V_(CC,n), g_(n)) values.

At event triggers, such as periodically or at transmitter 20 power orfrequency changes, the algorithm is repeated. As depicted in FIG. 10, ina Learning Sequence (block 102), new V_(CC) and ENV_(FB) values aremeasured from the feedback path 29, for N+1 defined interpolation nodes,and these values are stored. In an Interpolation Sequence (block 104),the gain of the RF PA 16 is calculated, and a nonlinear functionreflecting the actual gain (ENV_(FB)/V_(CC)) is constructed from thesefeedback data points, such as by using Newton's formula to construct apolynomial. The parameters defining the nonlinear function, such as thecoefficients of a Newton's polynomial, are calculated and stored.Subsequently, in an ongoing Computation Sequence (block 106), theamplitude envelope of a baseband transmission signal is multiplied bythe nonlinear function to control the power supply 14 to modulate asupply voltage V_(CC)(t) provided to the RF PA 16. The pre-distorted,envelope-tracking, modulated supply voltage V_(CC)(t) dynamicallymatches the power requirements of the RF PA 12 for the RF transmissionsignal being amplified, while maintaining a constant ISO-Gain. If thereis no event trigger, such as expiration of a periodic timer, RFfrequency change, or the like (block 108), then the Computation Sequence(block 106) is repeated—that is, it is an ongoing process. If an eventtrigger does occur (block 108), then the entire method 100 is repeated,with new parameters for the nonlinear function calculated from thefeedback path 29.

The ISO-Gain pre-distortion algorithm described herein was simulatedrecursively, and the gain linearity improvement tested at eachiteration. The simulations used a 5^(th)-order polynomial, and a LTE 10MHz full RB. The benefit of ISO-Gain is evaluated taking into account PA16 instantaneous gain; PA 16 instantaneous phase shifting; E_UTRAAdjacent Channels Power Ratio (ACPR); and UTRA ACPRs.

FIG. 11A depicts the evolution of the RF PA 16 supply voltage V_(CC)(t),and FIG. 11B depicts the evolution of the RF PA 16 instantaneous gain,after each iteration of the adaptive ISO-Gain algorithm. FIG. 11Aclearly depicts that as the number of iterations of the algorithmincrease, the RF PA 16 gain becomes increasingly constant versus time.As noted above, it is the decreases in V_(CC) that cause the greatestdips in PA 16 gain; multiple iterations of the adaptive pre-distortionalgorithm of embodiments of the present invention dramatically reducethese downward excursions in the gain. Furthermore, FIG. 11B shows thatan additional benefit of the adaptive pre-distortion algorithm disclosedherein is that dynamics of V_(CC) variations versus time is reduced.This reduction in dynamics improves the accuracy and performance of thepower supply 14.

FIGS. 12 and 13 depicts RF PA 16 gain and phases shift variations,respectively, as a function of instantaneous variations in the supplyvoltage V_(CC). After each iteration, both gain and phase shift becomemore and more constant, even though the supply voltage V_(CC) variesduring the time.

FIG. 14 depicts the output spectrum of the RF PA 16 without, and withone and two iterations of, the feedback-based, pre-distortion envelopetracking power control algorithm disclosed herein. Application of thealgorithm reduces spectral emissions outside of the 10 MHz band centredon the carrier frequency (indicated as 0 MHz in FIG. 14 due to thesimulator normalizing the spectrum frequency). The improvement isdetailed in Table 1 below.

TABLE 1 Step by Step ACPRs Pre- Output E UTRA UTRA 5 MHz UTRA 5 MHzdistortion Power ACPR (dBc) ACPR1 (dBc) ACPR2 (dBc) Iterations (dBm)High Low High Low High Low None 26.6 −26.9 −26.5 −27.7 −27.8 −31.9 −31.6One 26.4 −38.1 −37.7 −38.9 −38.9 −43.3 −42.9 Two 26.2 −43.6 −46.2 −44.8−44.7 −48.4 −48.1

Embodiments of the present invention present numerous advantages overprior art envelope tracking pre-distortion methods. By using feedback ofthe actual amplified signal, the methods disclosed herein can compensatefor nonlinearities in the entire transmitter 20 chain, not just the RFPA 16. Although described herein as benefitting the gain of the RF PA16, the adaptive ISO-Gain envelope tracking additionally improves phaseresponse of the RF PA 16. The method allows modifications to thepre-distortion applied to the supply power V_(CC)(t) as necessary, suchas when the transmitter 20 power or frequency changes, or as componentsage. The transmitter 20 is thus not reliant on factory calibrations, theelimination of which speeds and simplifies the manufacturing process.The pre-distortion calculations are not computationally intensive, incurlittle power consumption, and the calculated coefficients are stored ina very small, efficient LUT. Up to 17 dB improvement on ACPRs can beachieved with a 5^(th) order polynomial.

The present invention may, of course, be carried out in other ways thanthose specifically set forth herein without departing from essentialcharacteristics of the invention. The present embodiments are to beconsidered in all respects as illustrative and not restrictive, and allchanges coming within the meaning and equivalency range of the appendedclaims are intended to be embraced therein.

What is claimed is:
 1. An adaptive method of pre-distorting an envelopetracking modulation of supply voltage for a Radio Frequency (RF) poweramplifier (PA), comprising: calculating the amplitude envelope of acomplex baseband transmission signal; frequency up-converting thecomplex baseband transmission signal to RF; modulating a supply voltage,output by a dynamic power supply to a RF PA, in response to theamplitude envelope of the baseband transmission signal; amplifying theRF transmission signal by the RF PA receiving the modulated supplyvoltage; sampling an RF feedback signal at the RF PA output, frequencydown-converting the RF feedback signal to baseband and extracting anamplitude envelope of the baseband feedback signal; comparing theamplitude envelope of the baseband feedback signal with the amplitudeenvelope of the baseband transmission signal; and pre-distorting themodulation of the supply voltage in response to the comparison so as toachieve a constant gain in the RF PA, the pre-distorting being performedby executing: a Learning Sequence comprising sampling the basebandfeedback signal amplitude envelope at a plurality of predeterminedinterpolation nodes, an Interpolation Sequence comprising generating anonlinear polynomial function to fit the sampled interpolation nodevalues, and a Computation Sequence comprising multiplying the basebandtransmission signal amplitude envelope by the nonlinear polynomialfunction.
 2. The method of claim 1, wherein the polynomial is derivedfrom Newton's algorithm.
 3. The method of claim 1, wherein the Learningand Interpolation Sequences are performed periodically or at triggeringevents and coefficients to the nonlinear polynomial are stored; andwherein the Computation Sequence is performed on an ongoing basis topre-distort the modulation of the supply voltage so as to achieve aconstant gain in the RF PA.
 4. The method of claim 1, wherein theLearning Sequence further comprises generating a table of supply voltagevalues and corresponding baseband feedback signal amplitude envelopevalues at predefined interpolation nodes.
 5. The method of claim 4,wherein the Interpolation Sequence further comprises: calculating aplurality of RF PA gain values, each comprising a baseband feedbacksignal amplitude envelope value divided by a supply voltage levelcorresponding to baseband transmission signal amplitude envelope value;and calculating the coefficients of a polynomial derived from thecalculated RF PA gain values and the supply voltage levels.
 6. A RadioFrequency (RF) transmitter, comprising: a signal generator operative togenerate a complex baseband transmission signal; frequency up-convertingmixers operative to up-convert the baseband transmission signal to RF;an RF Power Amplifier (PA) operative to amplify the RF transmissionsignal; a dynamic power supply operative to provide a supply voltage tothe RF PA that is modulated to track an amplitude envelope of thebaseband transmission signal; a feedback loop operative to sample an RFfeedback signal at the RF PA output and frequency down-convert the RFfeedback signal to baseband; and a pre-distortion circuit operative tocalculate the gain of the RF PA based on the baseband feedback signaland the baseband transmission signal, and further operative to controlthe power supply to pre-distort the modulated supply voltage so as toachieve a constant gain in the RF PA, by executing: a Learning Sequencecomprising sampling the baseband feedback signal amplitude envelope at aplurality of predetermined interpolation nodes, an InterpolationSequence comprising generating a nonlinear polynomial function to fitthe sampled interpolation node values, and a Computation Sequencecomprising multiplying the baseband transmission signal amplitudeenvelope by the nonlinear polynomial function.
 7. The transmitter ofclaim 6 wherein the feedback loop comprises: an attenuator operative toattenuate the sampled RF feedback signal; frequency down-convertingmixers operative to down-convert the RF feedback signal to baseband; andan extraction circuit operative to calculate the amplitude envelope ofthe baseband feedback signal.
 8. The transmitter of claim 6, wherein thepolynomial is derived from Newton's algorithm.
 9. The transmitter ofclaim 6, wherein the pre-distortion circuit is operative to execute theLearning and Interpolation Sequences in response to a triggering eventand to store parameters for the nonlinear polynomial, and is operativeto execute the Computation Sequence on an ongoing basis to pre-distortthe modulation of the supply voltage so as to achieve a constant gain inthe RF PA.
 10. The transmitter of claim 6, wherein when executing theLearning Sequence, the pre-distortion circuit is further operative togenerate a table of supply voltage values and corresponding basebandtransmission signal amplitude envelope values at predefinedinterpolation nodes.
 11. The transmitter of claim 10, wherein whenexecuting the Interpolation Sequence, the pre-distortion circuit isfurther operative to: calculate a plurality of RF PA gain values, eachcomprising a baseband feedback signal amplitude envelope value dividedby a supply voltage level corresponding to a baseband transmissionsignal amplitude envelope value; and calculate the coefficients of apolynomial derived from the calculated RF PA gain values and the supplyvoltage levels.
 12. A non-transient computer readable media storingprogram instructions operative to pre-distort an envelope trackingmodulation of supply voltage for a Radio Frequency (RF) power amplifier(PA), the program instructions operative to cause a controller to:calculate the amplitude envelope of a complex baseband transmissionsignal; modulate a supply voltage, output by a dynamic power supply to aRF PA, in response to the amplitude envelope of the basebandtransmission signal; extract an amplitude envelope of a basebandfeedback signal sampled at the RF PA output and frequencydown-converted; calculate the RF PA gain from the amplitude envelope ofthe baseband feedback signal and the amplitude envelope of the basebandtransmission signal; and pre-distort the modulation of the supplyvoltage in response to the calculated gain so as to achieve a constantgain in the RF PA by executing: a Learning Sequence comprising samplingthe baseband feedback signal amplitude envelope at a plurality ofpredetermined interpolation nodes, an Interpolation Sequence comprisinggenerating a nonlinear polynomial function to fit the sampledinterpolation node values, and a Computation Sequence comprisingmultiplying the baseband transmission signal amplitude envelope by thenonlinear polynomial function.